An alternative (tree-based) semantics for a class of regular expressions
is proposed that assigns a central rôle to the + operator and thus to
nondeterminism and nondeterministic choice. For the new semantics a
consistent and complete axiomatization is obtained from the original
axiomatization of regular expressions by Salomaa and by Kozen by dropping
the idempotence law for + and the distribution law of • over +.